Distributed solution of the day-ahead pump and valve scheduling problem for dynamically adaptive water distribution networks with storage

This paper investigates the computation of daily schedules of pumps and boundary valves for the minimization of energy costs in water distribution networks (WDN) with dynamically adaptive configurations. The considered problem combines integer ("on"/''off'') pump control variables, non-convex energy conservation constraints and time-coupling mass conservation constraints. For operational WDNs, the resulting non-convex mixed- integer non-linear program (MINLP) is too large to be solved using available methods. We propose a tailored heuristic solution method based on the Alternating Direction Method of Multipliers which distributes and coordinates the solution of smaller problems corresponding to individual time steps of the original MINLP. The proposed method is applied to a large-scale WDN from the UK. The daily schedule of pumps and boundary valves obtained for the dynamically adaptive network configuration, computed in 12 min, is shown to beat most 6% suboptimal and nearly 5% cheaper than the globally optimal schedule corresponding to the traditional (sectorized) network configuration. The proposed algorithm outperforms alternative off-the-shelf and tailored approaches, providing a scalable method to compute good solutions to the complex day-ahead pump and valve scheduling problem in operational dynamically adaptive WDNs.